Applied math seminar: Takuji Ishikawa

March 8, 2023 @ 3:30 pm – 4:30 pm
Keller 302

Title: Hydrodynamics of Ciliary Swimming
Planktonic microorganisms are ubiquitous in water, and their population dynamics are essential for forecasting the behavior of global aquatic ecosystems. Their population dynamics are strongly affected by these organisms’ motility, which is generated by their hair-like organelles, called cilia or flagella. However, because of the complexity of ciliary dynamics, the precise role of ciliary flow in microbial life remains unclear.
In terms of fluid dynamics, ciliary swimming has been analyzed by using a squirmer model. A classical squirmer model propels itself by generating surface tangential and radial velocities. Recently, we developed a novel squirmer model in which, instead of a velocity being imposed on the cell surface, a shear stress is applied to the fluid on a stress shell placed slightly above the cell body. The shear stress expresses the thrust force generated by cilia, and the fluid must satisfy the no-slip condition on the cell body surface. The stress squirmer model has been successful in reproducing experimentally observed cell-cell interactions and cell-wall interactions.
In order to understand swimming energetics, we further developed a ciliate model incorporating the distinct ciliary apparatus. The hairy squirmer model revealed that over 90% of energy is dissipated inside the ciliary envelope. By using the hairy squirmer model, we found that there exists an optimal number density of cilia, which provides the maximum propulsion efficiency for all ciliates. The propulsion efficiency in this case decreases inversely proportionally to body length. Our estimated optimal density of cilia corresponds to those of actual microorganisms, including species of ciliates and microalgae, which suggests that now-existing motile ciliates and microalgae may have survived by acquiring the optimal propulsion efficiency.